Re: Threaded shaft length contraction paradox/contradiction?

On Mon, 16 Apr 2007 20:14:22 +0200, "Kees Roos" <croos@xxxxxxxxx>
wrote:


"David" <dseppala@xxxxxxxxxxxxx> schreef in bericht
news:edv323h253b6mdhdgp3c69m958qbrgtpog@xxxxxxxxxx
Can anyone explain how to apply Einstein's notions of space and time
to the following length contraction problem?

What's wrong with your own explanation?

Let there be a long threaded shaft along the x-axis, or in other words
a very long threaded bolt aligned along the x-axis. In the rest frame
of this shaft, let there be 1000 threads per meter along the shaft.
Let there be a nut of length L on this shaft that also has 1000
threads per meter. Initially, let both the shaft and nut be at rest.

Now start spinning the nut. Because of the nut's spin, the nut
travels down the shaft at some velocity V.

As measured in the rest frame of the shaft, per Einstein, the nut
should span a length less than L, but that would mean the 1000 threads
of the nut span less than 1000 threads of the shaft. Or as measured
in the frame that has zero velocity with respect to the nut's motion
along the length of the shaft, the 1000 threads of the nut span a
length on the shaft that has more than 1000 threads. I don't see how
either of these is possible.

So, this is your explanation. Nothing wrong so far.

If I attempt to make some sort of argument about the nut being
stretched or compressed so that both the nut and shaft always
simultaneously span the same number of threads, then I don't see how
to apply Einstein's notions of simultaneous events in the two moving
frames. If I simply count the number of threads on the nut and then
mark two points of the shaft that span the same number of threads, if
both frames agree that the nut simultaneously spans these two points,
then Einstein's notion of simultaneous events for these two frames
doesn't work.

Why going to all this trouble? In your scenario the nut does no longer fit
the bolt.
What is the paradox? What is the contradiction?
In the rest frame of the bolt, the number of threads of the nut does
not change, since all points of the rotation were started
simultaneously. There is no point in this process where the nut jumps
over threads to span less threads (length contracted) of the bolt. I
posted a possible response to Jeckyl suggesting that the nut must
undergo a physical stretching in this scenario and the threads keep it
stretched so that it never returns to what the rest frame would expect
its length to be to explain what is happening.
Most responders either post psychological thoughts about me or
non-sense physical hypotheses because they think relativistic effects
only occur when V approaches c.
David

Thanks,
David Seppala
.

Relevant Pages

  • Re: Threaded shaft length contraction paradox/contradiction?
    ... of this shaft, let there be 1000 threads per meter along the shaft. ... let both the shaft and nut be at rest. ... As measured in the rest frame of the shaft, per Einstein, the nut ... of the nut span less than 1000 threads of the shaft. ...
    (sci.physics.relativity)
  • Re: Threaded shaft length contraction paradox/contradiction?
    ... Let there be a long threaded shaft along the x-axis, ... let both the shaft and nut be at rest. ... of the nut span less than 1000 threads of the shaft. ... Nuts and bolts are made loose enough in their fit to spin freely. ...
    (sci.physics.relativity)
  • Re: Threaded shaft length contraction paradox/contradiction?
    ... Let there be a long threaded shaft along the x-axis, ... let both the shaft and nut be at rest. ... As measured in the rest frame of the shaft, per Einstein, the nut ... of the nut span less than 1000 threads of the shaft. ...
    (sci.physics.relativity)
  • Re: Threaded shaft length contraction paradox/contradiction?
    ... Let there be a long threaded shaft along the x-axis, ... let both the shaft and nut be at rest. ... of the nut span less than 1000 threads of the shaft. ... both frames agree that the nut simultaneously spans these two points, ...
    (sci.physics.relativity)
  • Re: Threaded shaft length contraction paradox/contradiction?
    ... Let there be a long threaded shaft along the x-axis, ... let both the shaft and nut be at rest. ... As measured in the rest frame of the shaft, per Einstein, the nut ...
    (sci.physics.relativity)